1.Intergranular fracture of steels can occur under a variety of metallurgical conditions.Discuss in detail three distinct causes of Intergranular fracture. Describe the characteristics of the various modes by which a structural transformation that involves no compositional change can take place in binary metallic alloys. 3. (a)What is the mechanism by which dislocations surmount the Peierls barrier in a crystal?What assumptions are involved in describing the process?What are the reasons for the Peierls barrier being effective at successively higher values of T/Tm,where Tm is the melting temperature,for fcc metals,bcc metals,and diamond-cubic semi-metals,respectively? (b)Why does the effective line tension differ for a bowing-out,initially screw-oriented dislocation and screw dislocation decreasing in length?Which line tension is larger? 4. a)Discuss in detail the operation of Frank-Read source for dislocation segment pinned by(a)super jogs and(b)5 um second phase particles.Is this model applicable in real systems?Has it been observed experimentally?What approximations are involved in the quantitative description of the process? b)For what types of metals and material and under what conditions of system variables is the Peierls barrier important in metal deformation?What is the specific mechanism for its influence on mechanical properties? 5.(a)Discuss the process of intersection of two perpendicular screw dislocations. In what temperature and strain regime would you expect this process to be important?Why? (b)What is the Peach-Koehler equation for the force on a dislocation?Illustrate its use dor the case of glide interaction of two edge dislocation with the same slip system but whose glide planes are separated by a normal distance h. 6. Discuss critically,proposed mechanisms for the initiation of the cellular microstructure in discontinuous precipitation reactions. 7.The individual particles of atomized aluminum and titanium alloys are coated with a thin oxide film.Discuss the effects of the oxide film on the processing (cold compaction,hot pressing,extrusion,welding)and mechanical properties of the consolidated powder. 8.Discuss in detail the process of cross-slip in a brass.For an exact calculation of the energy barrier,describe how you would proceed.Illustrate your best guess of the critical configuration.How would the process depend on dislocation character?
1. Intergranular fracture of steels can occur under a variety of metallurgical conditions. Discuss in detail three distinct causes of Intergranular fracture. 2. Describe the characteristics of the various modes by which a structural transformation that involves no compositional change can take place in binary metallic alloys. 3. (a) What is the mechanism by which dislocations surmount the Peierls barrier in a crystal? What assumptions are involved in describing the process? What are the reasons for the Peierls barrier being effective at successively higher values of T/Tm, where Tm is the melting temperature, for fcc metals, bcc metals, and diamond-cubic semi-metals, respectively? (b) Why does the effective line tension differ for a bowing-out, initially screw-oriented dislocation and screw dislocation decreasing in length? Which line tension is larger? 4. a) Discuss in detail the operation of Frank-Read source for dislocation segment pinned by (a) super jogs and (b) 5 μm second phase particles. Is this model applicable in real systems? Has it been observed experimentally? What approximations are involved in the quantitative description of the process? b) For what types of metals and material and under what conditions of system variables is the Peierls barrier important in metal deformation? What is the specific mechanism for its influence on mechanical properties? 5. (a) Discuss the process of intersection of two perpendicular screw dislocations. In what temperature and strain regime would you expect this process to be important? Why? (b) What is the Peach-Koehler equation for the force on a dislocation? Illustrate its use dor the case of glide interaction of two edge dislocation with the same slip system but whose glide planes are separated by a normal distance h. 6. Discuss critically, proposed mechanisms for the initiation of the cellular microstructure in discontinuous precipitation reactions. 7. The individual particles of atomized aluminum and titanium alloys are coated with a thin oxide film. Discuss the effects of the oxide film on the processing (cold compaction, hot pressing, extrusion, welding) and mechanical properties of the consolidated powder. 8. Discuss in detail the process of cross-slip inα brass. For an exact calculation of the energy barrier, describe how you would proceed. Illustrate your best guess of the critical configuration. How would the process depend on dislocation character?
9 (a)The introduction of discrete defects into an otherwise elastic solid containing a large sharp crack can either increase or decrease the apparent fracture toughness of the solid.Describe the physical basis common to both effects. (b)What effect will a dislocation withb=10=001]have on the Mode I stress intensity factor of a crack on the (010)plane with crack front parallel to [0011.This dislocation is located directly ahead (=0)of the crack.Given: cos -sin e sin 301 √2πr 2 2 2 e. 0.38 022=- -cos-[l+sin。sin 2πr 2 2 62 K,-sin号cos2co .0030 2πr2 2 2 (c)Ignoring the areal fraction contribution,will an array of small internally pressurized bubbles,uniformly distributed in the matrix,affect the fracture toughness of steel below the NDT?Explain. 10.Discuss the motion of the dislocations shown in each of cases below.Be as quantitative as possible,discussing the particular path of motion the dislocation will take,showing detailed expressions where possible, explaining your steps,and interpreting your results.Assume that the direction of dislocation motion coincides with direction of dislocation motion coincides with the direction of force acting on the dislocation. Hint:The Peach-Koehler equation defining the force exerted on a unit length of dislocation line with direction s and Burgers vector b,due to an external stress fieldo,is: R =(o·b)×5 L Case(a) A specimen of uniform thickness with a dislocation located at position (xl=a, x2=b)from a corner,and defined by b=bes 5=e3
9. (a) The introduction of discrete defects into an otherwise elastic solid containing a large sharp crack can either increase or decrease the apparent fracture toughness of the solid. Describe the physical basis common to both effects. (b) What effect will a dislocation with , have on the Mode I stress intensity factor of a crack on the (010) plane with crack front parallel to [001]. This dislocation is located directly ahead ( b b [ ] 100 → = ξ [001] → = θ = 0) of the crack. Given: 11 22 33 3 cos [1 sin sin ] 2 2 2 3 cos [1 sin sin ] 2 2 2 3 sin cos cos 2 22 2 I I I K r K r K r 2 2 θ θ θ σ π θ θ θ σ π θθ θ σ π = − = + = (c) Ignoring the areal fraction contribution, will an array of small internally pressurized bubbles, uniformly distributed in the matrix, affect the fracture toughness of steel below the NDT? Explain. 10. Discuss the motion of the dislocations shown in each of cases below. Be as quantitative as possible, discussing the particular path of motion the dislocation will take, showing detailed expressions where possible, explaining your steps, and interpreting your results. Assume that the direction of dislocation motion coincides with direction of dislocation motion coincides with the direction of force acting on the dislocation. Hint: The Peach-Koehler equation defining the force exerted on a unit length of dislocation line with direction ξ and Burgers vector b, due to an external stress fieldσ , is: ( ) F b L = σ ⋅ ×ξ Case (a) A specimen of uniform thickness with a dislocation located at position (x1=a, x2=b) from a corner, and defined by 3 3 ˆ ˆ b be ξ e = =
。(a,b) e1 Free Surfaces Case(b) A specimen thinned down in the e,~direction,under tensile loading o.The dislocation is very far from all surfaces,except the upper and lower surfaces into which the dislocation runs.The dislocation and stress field are defined by: b=be 5=e =e(ie.,is the only nonzero component of stress) 3-D view applied stress 2 front view showing important diΠiensi0ns 11. Describe the role of stress(static and cyclic)in metallic corrosion phenomena. Discuss the use of fracture mechanics. 12. There is a long-standing interest in adding ceramic "particles"to metal matrices.Some examples of such commercial materials are WC-Co cermets, Al-SiC composites,and TD-nickel(thoria dispersed nickel).Describe in detail the various strengthening mechanisms that are possible in such systems(at both low and high temperature).Clearly delineate the ranges of particle size and volume fraction at which each mechanism operates.Also describe how the material behavior changes when such particles are added. 13. With the aid of suitable diagrams,deduce the types of monoclinic Bravais
Case (b) A specimen thinned down in the ~direction, under tensile loading 3 eˆ σ . The dislocation is very far from all surfaces, except the upper and lower surfaces into which the dislocation runs. The dislocation and stress field are defined by: 1 2 ˆ ˆ b be ξ e = = 1 1 σ = σe eˆ ˆ (i.e., σ11 is the only nonzero component of stress) 11. Describe the role of stress (static and cyclic) in metallic corrosion phenomena. Discuss the use of fracture mechanics. 12. There is a long-standing interest in adding ceramic "particles" to metal matrices. Some examples of such commercial materials are WC-Co cermets, Al-SiC composites, and TD-nickel (thoria dispersed nickel). Describe in detail the various strengthening mechanisms that are possible in such systems (at both low and high temperature). Clearly delineate the ranges of particle size and volume fraction at which each mechanism operates. Also describe how the material behavior changes when such particles are added. 13. With the aid of suitable diagrams, deduce the types of monoclinic Bravais
lattices which may be obtained from the stacking of two-dimensional lattices. 14.Write an essay which describes and explains the effects due to grain boundaries during precipitation from solid solution. 15.Consider a straight edge dislocation in a crystal.Discuss the types of forces that can operate on the dislocation.For one type of force,give an explicit answer in terms of the Peach-Koehler formula. 16.Discuss in detail the classification of types of kinks on dislocations,the physical basis for their presence on dislocations,and macroscopic properties that indicate the presence of kinks.Give an expression for the velocity of a dislocation moving under a rate-controlling process of kink formation. 17. Consider cleavage fracture of a single crystal of LiF.The crack plane Is the (001)and the crack front-lies parallel to the [100]direction.The surface energy of LiF Is .35 j/m and the slip systems are a/2 <110>{110).Assume cross slip does not occur. (a)Assuming Jc >2y,predict the characteristics(size,shape,dislocation makeup) of the plastic zone as the applied J Increases from zero to above 2Y.Also, describe any distinguishing differences between the surface zone and the midthickness zone. (b)If the material is altered in some way such that J>2Y,what happens to the plastic zone? (c)Assuming that J=2y (exactly),sketch and describe the loading/unloading load-displacement curve for a cracked single crystal DCB specimen with an Initial slot of length a(and"a"can't be less than a )In constructing your sketch assume that crack extension occurs. 18. Discuss the microstructural basis for the Orowan-Friedel relation.Consider the validity of the relation in view of the approximations involved In its derivation.For what types of microstructural features should the relation apply? 15.(a)Symmetry axes are sometimes described in terms of rotation axes and rotation-reflection axes.rather than rotation axes and inversion axes.The operation of a rotation-reflection axis Sn consists of a rotation through 27/n followed by reflection in a plane normal to the rotation-reflection axis.Sketch stereograms showing the operation of 1,2,3,4,and 6-fold reflection axes on a single pole in a general position.Deduce the inversion axis to which each is equivalent. (b)Pure Au and pure Cu are both cubic with atoms at 0,0,0;0,1/2,1/2;1/2,0,1/2; 1/2,1/2,0.The compound Cu-Au is cubic with an Au atom at 0,0,0 and Cu atoms at 0,1/2,1/2;1/2,0,1/2;1/2,1/2,0.Determine the lattice type of Au,Cu,and Cu3Au,and in each case state the number of atoms associated with each lattice
lattices which may be obtained from the stacking of two-dimensional lattices. 14. Write an essay which describes and explains the effects due to grain boundaries during precipitation from solid solution. 15. Consider a straight edge dislocation in a crystal. Discuss the types of forces that can operate on the dislocation. For one type of force, give an explicit answer in terms of the Peach-Koehler formula. 16. Discuss in detail the classification of types of kinks on dislocations, the physical basis for their presence on dislocations, and macroscopic properties that indicate the presence of kinks. Give an expression for the velocity of a dislocation moving under a rate-controlling process of kink formation. 17. Consider cleavage fracture of a single crystal of LiF. The crack plane Is the (001) and the crack front-lies parallel to the [100] direction. The surface energy of LiF Is .35 j/m and the slip systems are a/2 <110> {110}. Assume cross slip does not occur. (a) Assuming Jc > 2y , predict the characteristics (size, shape, dislocation makeup) of the plastic zone as the applied J Increases from zero to above 2Y. Also, describe any distinguishing differences between the surface zone and the midthickness zone. (b)If the material is altered in some way such that J→2Y, what happens to the plastic zone? (c) Assuming that J = 2y (exactly) , sketch and describe the loading/unloading load-displacement curve for a cracked single crystal DCB specimen with an Initial slot of length a (and “a” can't be less than a ). In constructing your sketch assume that crack extension occurs. 18. Discuss the microstructural basis for the Orowan-Friedel relation. Consider the validity of the relation in view of the approximations involved 1n its derivation. For what types of microstructural features should the relation apply? 15. (a) Symmetry axes are sometimes described in terms of rotation axes and rotation-reflection axes, rather than rotation axes and inversion axes. The operation of a rotation-reflection axis Sn consists of a rotation through 2π /n followed by reflection in a plane normal to the rotation-reflection axis. Sketch stereograms showing the operation of 1, 2, 3, 4, and 6-fold reflection axes on a single pole in a general position. Deduce the inversion axis to which each is equivalent. (b) Pure Au and pure Cu are both cubic with atoms at 0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0. The compound Cu-Au is cubic with an Au atom at 0,0,0 and Cu atoms at 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0. Determine the lattice type of Au, Cu, and Cu3Au, and in each case state the number of atoms associated with each lattice
point. 16. Discuss the influence of kinks and jogs on dislocation motion.Qualitatively compare the regimes of temperature where these defects could be important in metals and in cubic (Ge and Si)materials 17. Consider the two dislocations shown in the figure below.Dislocation A is at the origin of global Cartesian coordinate system (x),and dislocation B is positioned at x1=2,x2=1.A second Cartesian coordinate system (x')has origin at dislocation B,and is oriented relative to the global coordinate system by a counterclockwise rotation of 45 about die x3-axis.The two dislocations have Burgers vector b and dislocation line g;described by: b4=2[100] Referred to the global (x) 54=-[00则 coordinate system. b=[100] Referred to the local (x') B=1[001] coordinate system. Use me pictorial,mathematical,and textual information to answer the following questions: (a)What are the components of the stress field caused by dislocation A at the dislocation B position,as referred to global(x)coordinate system? (b)What are the components of me stress field caused by dislocation A at the dislocation B position,as referred to me local(x')coordinate system? (c)What are the glide and climb directions of dislocation B,as referred to the local (x')coordinate system? (d)What arc the glide and climb forces,as referred to the local (x')coordinate system,that act on dislocation B due to the presence of dislocation A?Show your basic equations and steps carefully. 18. A thin,linear-elastic film of thickness h is deposited on a thick,linear-elastic substrate.A two-dimensional representation of the assembly is shown below. free surface film interface substrate The stress-free lattice spacing af of the film in the e^-direction is less than the corresponding spacing as in the substrate,and this produces a uniform tensile coherency strain(as-af)/af in the film when the interface is coherent.The thickness h is small enough to assume uniform stresses and strains through the thickness of the film.Further,the whole sample is very thick in thein-
point. 16. Discuss the influence of kinks and jogs on dislocation motion. Qualitatively compare the regimes of temperature where these defects could be important in metals and in cubic (Ge and Si) materials. 17. Consider the two dislocations shown in the figure below. Dislocation A is at the origin of global Cartesian coordinate system (x), and dislocation B is positioned at x1=2, x2=l. A second Cartesian coordinate system (x') has origin at dislocation B, and is oriented relative to the global coordinate system by a counterclockwise rotation of 45° about die x3-axis. The two dislocations have Burgers vector b and dislocation line ξ ; described by: 2[100] -l[00l] [100] 1[001] A A B B b b ξ ξ = = = = Referred to the global (x) coordinate system. Referred to the local (x') coordinate system. ⎧ ⎨ ⎩ ⎧ ⎨ ⎩ Use me pictorial, mathematical, and textual information to answer the following questions: (a) What are the components of the stress field caused by dislocation A at the dislocation B position, as referred to global (x) coordinate system? (b) What are the components of me stress field caused by dislocation A at the dislocation B position, as referred to me local (x') coordinate system? (c) What are the glide and climb directions of dislocation B, as referred to the local (x') coordinate system? (d) What arc the glide and climb forces, as referred to the local (x') coordinate system, that act on dislocation B due to the presence of dislocation A? Show your basic equations and steps carefully. 18. A thin, linear-elastic film of thickness h is deposited on a thick, linear-elastic substrate. A two-dimensional representation of the assembly is shown below. The stress-free lattice spacing af of the film in the e^-direction is less than the corresponding spacing as in the substrate, and this produces a uniform tensile coherency strain 11 ε = (as-af)/af in the film when the interface is coherent. The thickness h is small enough to assume uniform stresses and strains through the thickness of the film. Further, the whole sample is very thick in the 3e -in-